`P Q` and `R S` are two parallel chords of a circle whose centre is `O` and radius is `10c mdot` If `P Q=16c m` and `R S=12c m ,` find the distance between `P Q` and `R S ,` if they lie: on the same side of the centre `Odot` on opposite side of the centre `Odot`

Explanation

To solve the problem, we need to find the distance between the two parallel chords \(PQ\) and \(RS\) of a circle with a radius of \(10 \, \text{cm}\). We are given that the lengths of the chords are \(PQ = 16 \, \text{cm}\) and \(RS = 12 \, \text{cm}\). We will solve this for two cases: when the chords are on the same side of the center \(O\) and when they are on opposite sides.

### Step-by-Step Solution:

#### Case 1: Chords on the Same Side of the Center

1. **Identify the half-lengths of the chords**:
- For chord \(PQ\):
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